Statistics Question

Question

The lengths of a runner's workout have a continuous uniform distribution between 49.29 min and 55.55 min. If one such workout is randomly selected, find P₄₉

P₄₉ =

(Report answer accurate to 4 decimal places when needed.)

Answer 1

The function is continuous Uniform distribution between 49.29 min and 55.55 minutes. So the probability that the random variable (the length of runner workout in this example) takes values outside these two values will be zero.

Since for a continuous distribution, the probability that random variable x takes a specific value is equal to zero, the P(x=49) =0.

Also, the P(x<=49) will also be zero because as mentioned above, this uniform distribution has a 0 probability everywhere except between 49.29 and 55.55 min.